On Auslander-Reiten components of string complexes for a certain class\n of symmetric special biserial algebras

2020/04/02 by Hernán Giraldo, Giraldo, Hernán A., Ricardo Rueda-Robayo +3
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2004.01296

openalex publication_date 2020/04/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \k be an algebraically closed field. In this article, inspired\nby the description of indecomposable objects in the derived category of a\ngentle algebra obtained by V. Bekkert and H. A. Merklen, we define string\ncomplexes for a certain class mathscrC of symmetric special biserial\nalgebras, which are indecomposable perfect complexes in the corresponding\nderived category. We also prove that if \Λ is a \k-algebra in\nthe class mathscrC and P^ bullet is a string complex over \Λ,\nthen P^ bullet lies in the rim of its Auslander-Reiten component.\n

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